An efficient polar coordinate system Fourier transform algorithm

The problem of efficiently computing the discrete Fourier transform (DFT) of data acquired in an r= theta polar coordinate system has received considerable attention over the last 30 years. The interest in the problem has come from several different fields, including antenna and RCS (radar cross section) measurements, radio astronomy, and medical imaging. The author presents an alternative algorithm that offers advantages in some circumstances, particularly when it is desirable to process a limited number of theta angles. This algorithm transforms data from samples evenly spaced in r at arbitrary theta angles to an evenly spaced Cartesian spectrum. In order to verify the validity of the zero-order hold interpolation scheme, a test was performed to see how well the inverse transformation could reproduce an original distribution. A full-resolution aperture was synthesized with a uniform illumination and transformed using the polar Fourier transform algorithm combined above, padding the 1D fast Fourier transforms to eight times the output dimensions.<>